Each Ann-category $\A$ is equivalent to an Ann-category of the type $(R,M),$ where $M$ is an $R$-bimodule. The family of constraints of $A$ induces a { \it structure} on $(R,M).$ The main result of the paper is: 1. { \it There exists a bijection between the set of structures on $(R,M)$ and the group of Mac Lane 3-cocycles $Z^{ 3}_{ MaL}(R, M).$} 2. { \it There exists a bijection between $C(R,M)$ of congruence classes of Ann-categories whose pre-stick is of the type $(R,M)$ and the Mac Lane cohomology group $H^3_{ \textrm{ MaL}}(R,M).$}
Categories: math.CT